Question: Subtract the following rational expressions. $\dfrac{m^3+26}{-5m^2+19}-\dfrac{2m^3+13}{-5m^2+19}=$
Explanation: We want to subtract two rational expressions whose denominators are equal. We can do this by subtracting the numerators and keeping the denominator the same. [Does this fit with how we subtract rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{m^3+26}{-5m^2+19}-\dfrac{2m^3+13}{-5m^2+19} \\\\ &=\dfrac{(m^3+26)-(2m^3+13)}{-5m^2+19} \\\\ &=\dfrac{m^3+26-2m^3-13}{-5m^2+19} \\\\ &=\dfrac{-m^3+13}{-5m^2+19} \end{aligned}$ In conclusion, $\dfrac{m^3+26}{-5m^2+19}-\dfrac{2m^3+13}{-5m^2+19}=\dfrac{-m^3+13}{-5m^2+19}$